Philosophy of Physics Seminar (Thursday - Week 7, HT25)

Abstract: A theory’s possessing symmetries often indicates that its models exhibit surplus structure. This in turn suggests that the theory is in need of reformulation. Two approaches to reformulation found in the literature are reduction and sophistication. Recently, sophistication has become more popular than reduction. Defenders of sophistication allege that reductions are difficult to find and frequently not as attractive as rival sophistications. I argue however that this impression arises from an overly restrictive way of thinking about reductions. It is commonly held that a reduction of a theory must be formulated explicitly in terms of symmetry-invariant quantities of that theory, and that it must be empirically equivalent to the original. On the basis of a success case of reformulation, viz. the reformulation of Newtonian Gravitation Theory due to Barbour and Bertotti, I argue that reductions need not meet these criteria. This leads to a more inclusive and fruitful way of thinking about reduction. I illustrate the strengths of this wider conception by demonstrating that it allows us to reduce Newtonian Gravitation Theory with respect to its scale symmetry - a symmetry that poses a particular challenge for the reduction strategy. The resulting theory is arguably superior to its sophisticated rival.